Properties of the LWR model with time delay
DOI10.3934/nhm.2020032zbMath1469.35145arXiv2003.12090OpenAlexW3110959819MaRDI QIDQ2040870
Elisa Iacomini, Thomas Jung, Simone Goettlich
Publication date: 14 July 2021
Published in: Networks and Heterogeneous Media (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.12090
numerical simulationsmacroscopic traffic flow modelshyperbolic delay partial differential equationLax-Friedrichs discretizationstop \& go waves
Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Traffic problems in operations research (90B20) Traffic and pedestrian flow models (76A30)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the micro-to-macro limit for first-order traffic flow models on networks
- Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity
- Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic
- Macroscopic models for vehicular flows and crowd dynamics: theory and applications. Classical and non-classical advanced mathematics for real life applications
- On the micro-macro limit in traffic flow
- Kinetic models for traffic flow resulting in a reduced space of microscopic velocities
- Traffic dynamics and simulation. Data models and applications of traffic flow dynamics.
- A delay-differential equation model of HIV infection of \(\text{CD}4^+\) T-cells
- Measure-valued solutions to nonlocal transport equations on networks
- The BGK approximation of kinetic models for traffic
- Nonlocal conservation laws with time delay
- The time delays' effects on the qualitative behavior of an economic growth model
- An interface-free multi-scale multi-order model for traffic flow
- Derivation of second order traffic flow models with time delays
- A Godunov type scheme for a class of LWR traffic flow models with non-local flux
- Well-posedness of a conservation law with non-local flux arising in traffic flow modeling
- A General Phase Transition Model for Vehicular Traffic
- Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
- Non local balance laws in traffic models and crystal growth
- Feedback stabilization of linear systems with delayed control
- From Traffic and Pedestrian Follow-the-Leader Models with Reaction Time to First Order Convection-Diffusion Flow Models
- Hyperbolic Phase Transitions in Traffic Flow
- Resurrection of "Second Order" Models of Traffic Flow
- A Nonlinear Discrete Velocity Relaxation Model For Traffic Flow
- A measure theoretic approach to traffic flow optimisation on networks
- A mixed ODE–PDE model for vehicular traffic
- Shock Waves on the Highway
- Nonlinear Effects in the Dynamics of Car Following
- An Introduction to Delay Differential Equations with Applications to the Life Sciences
- On kinematic waves II. A theory of traffic flow on long crowded roads
This page was built for publication: Properties of the LWR model with time delay
